Simon
A contigency is a statement that cannot be deduced trough logic, that is, there's not enough applications to reduce all abstractions. Btw haven't you said once that abstractions do not exist, or that abstractions cannot be percepted? Here's an example of a tautology:
not (p and not p)
this is an abstraction because of the variable p, however if we apply any p we see that we can reduce it to true. Because its true for any p, the whole statement is true, and thus a tautology.
p and q
is a contigency because its an abstraction with two variables p and q, and it cannot be deduced to true. However if we choose a p and a q we can deduce it either to true or false.
Suppose that the universe consisted of two entitities, you and a turing machine representing the universe.
The only way of communication between you and the universe is, that you ask a yes/no question and the UTM answers either yes or no. Also UTM cannot answer yes and no on the same question.
for instance:
MIND: p="I see a cat", is p true? --> | <-- Yes : UTM
now how do i formulate the gödel sentence if UTM is unknown, simple, we assume that you will get the answer if UTM exists.
MIND: g="do I not get the answer yes" is g true? --> | <--... : UTM
MIND: f="ah I see that g is true" is f true? --> | <--Yes : UTM
It looks like UTM is incomplete, but couldn't it be that the question never passed the barrier | in between? | denoting the interface between UTM and MIND that allows this communication.
In the next question you ask if you see that g is true, and UTM answers yes, this means that you think g is true, but UTM doesn't say if its true nevertheless, it lets you think that its true. This suggest that MIND is inconsistent, however MIND is not a turing machine, it does not emmit information to UTM, it only percepts information from UTM, it only asks UTM questions, not state anything. The fundamental difference between MIND and UTM is that MIND asks and UTM answers.
Now lets make a set of questions that MIND can ask. We'll make a lamda function that takes any of these questions and returns an answer. Note that MIND cannot ask if a contigency is true, because the truth of contigencies cannot be percepted, only tautologies. Why is this?
We have assumed that all of MIND's perceptions are Yes/no answers to MIND's questions, in other words we cannot experience anything else. Thus its possible to experience f but not possible to experience g.
MIND cannot do any information processing on its own, it can only experience the deduction trough UTM, and f is not a deduction, it could be called intuition, but its still an experience which UTM offers. Its similar to the experience you mentioned about the cat, you saw what seemed to be a cat but later on you were certain that you were delusional.
My point is that UTM is not UTM unless it can stand for all of your experiences, including the intuitive truth of gödel's sentence. Btw I do not experience it at all, it must only go for certain minds. I for instance haven't seen dogs that i first though were cats either.
